Clinical assessment routinely uses terms such as development, growth trajectory, degeneration, disease progression, recovery or prediction. This terminology inherently carries the aspect of dynamic processes, suggesting that single measurements in time and cross-sectional comparison may not sufficiently describe spatiotemporal changes. In view of medical imaging, such tasks encourage subject-specific longitudinal imaging. Whereas follow-up, monitoring and prediction are natural tasks in clinical diagnosis of disease progression and of assessment of therapeutic intervention, translation of methodologies for calculation of temporal profiles from longitudinal data to clinical routine still requires significant research and development efforts. Rapid advances in image acquisition technology with significantly reduced acquisition times and with increase of patient comfort favor repeated imaging over the observation period. In view of serial imaging ranging over multiple years, image acquisition faces the challenging issue of scanner standardization and calibration which is crucial for successful spatiotemporal analysis. Longitudinal 3D data, represented as 4D images, capture time-varying anatomy and function. Such data benefits from dedicated analysis methods and tools that make use of the inherent correlation and causality of repeated acquisitions of the same subject. Availability of such data spawned progress in the development of advanced 4D image analysis methodologies that carry the notion of linear and nonlinear regression, now applied to complex, high-dimensional data such as images, image-derived shapes and structures, or a combination thereof. This paper provides examples of recently developed analysis methodologies for 4D image data, primarily focusing on progress in areas of core expertise of the authors. These include spatiotemporal shape modeling and growth trajectories of white matter fiber tracts demonstrated with examples from ongoing longitudinal clinical neuroimaging studies such as analysis of early brain growth in subjects at risk for mental illness and neurodegeneration in Huntington's disease (HD). We will discuss broader aspects of current limitations and need for future research in view of data consistency and analysis methodologies.